The invention relates to a method and arrangement for determining the delivery flow of a pump.
The delivery of a pump is an important operating variable. It is possible to measure the delivery flow directly. Here, use is often made of e.g. magnetic inductive flow meters. These flow meters are often very costly and require additional technical outlay.
A further option for determining the delivery flow consists of indirect methods. Here, use is made of delivery head-delivery flow relationships of the pump, which are also known as H(Q) characteristics. In these delivery head-delivery flow relationships, the delivery head H is plotted against the delivery flow Q.
Further characteristics which are used for determining the delivery indirectly are the power-delivery flow relationships of the pump, which are also referred to as P(Q) characteristics.
The manufacturer ascertains such characteristics, particularly in the case of centrifugal pumps. The characteristic form of the characteristic depends on the pump design, such as impeller, pump casing and rotational speed.
When determining the delivery indirectly by way of H(Q) characteristics and/or P(Q) characteristics, said determination is difficult if the characteristics have a very flat profile or initially increase and then drop off again. In the case of flat characteristics, the ascertained delivery flow is afflicted with a large error since very small deviations in the delivery head or power already lead to very large changes in the ascertained delivery flow.
By way of example, if the delivery should be determined from the pressure difference between pressure side and suction side of the pump by way of an H(Q) characteristic, the latter must be unique. Here, exactly one Q value must be assignable to each H value. This condition is often not satisfied in practice. The H(Q) characteristics are either too flat or initially have a rise and then drop again, and so two delivery flow values are assignable to each H value. The problem also exists if the delivery is intended to be determined by the measured power uptake from the P(Q) characteristic. The curves of such P(Q) characteristics are also often flat and non-unique.
International patent document no. WO 2005/064167 A1 describes a method for an internal amount measurement of a centrifuge pump using pressure recorders. The pressure recorders capture the difference pressure generated by the centrifuge pump. The delivery Q is ascertained from the difference pressure by means of a unit. Here, use is made of both the delivery head and the power.
German patent document no. DE 10 2009 022 107 A1 describes a method for determining the operating point of a centrifuge pump. Here, operating-point-dependent measurement variables are captured by sensors and evaluated during the operation. The operation is determined from mechanical measurement variables. A frequency analysis is used to ascertain a frequency which is linearly proportional to the rotational sound of the pump. The rotational speed is ascertained from the frequency, wherein the operating point is determined from the slip-dependent rotational speed/torque dependence of the asynchronous motor.
It is an object of the invention to specify a method for determining the delivery flow, said method being reliable and connected with as little instrumentation outlay as possible. The method should supply reliable values for the delivery flow, even the case of pumps with flat characteristics. Error sources should be minimized in the process.
According to the invention, this object is achieved by virtue of initially ascertaining the values for the delivery head, more specifically for the so-called reduced delivery head, and for the power of the pump. The reduced delivery head is understood to mean the delivery head reduced by the speed-dependent component—which is initially still unknown on account of the yet to be determined delivery. The reduced delivery head is referred to as delivery head below for reasons of simplicity. A probability density function is then calculated for each of delivery head and power by way of a functional relationship. A first probability density function for the delivery flow is ascertained from a delivery head-delivery flow relationship and from the probability density function for the delivery head. A second probability density function for the delivery flow is ascertained from a power-delivery flow relationship and the probability density function for the power. A combined probability density function is ascertained in a next step from the first probability density function and the second probability density function for the delivery flow. The delivery flow is determined from this combined probability density function.
According to the invention, the data from the delivery head-delivery flow relationship are fused with data from the power-delivery flow relationship in such a way that errors in determining the delivery flow are minimized in a targeted manner. In contrast to conventional methods, it is not the case that a first value for the delivery flow is initially developed from an H(Q) characteristic, followed by a second value for the delivery flow, which is completely independent thereof, being developed from a P(Q) characteristic; instead, the data is fused by way of probability density functions in this sensor data fusion according to the invention.
The method according to the invention supplies particularly accurate and stable values for the delivery flow. Here, decisive advantage consists of an ideal weighting of the characteristics depending on the quality thereof. In the case of characteristic lines extending in a flat manner, a small deviation in the delivery head or in the power leads to large errors in the delivery flow. By applying the probability density functions, the characteristic with a flatter curve in the vicinity of the current operating point is automatically weighted less strongly in the method according to the invention than the characteristic with the steeper curve. The steeper the curve in the vicinity of the current operating point, the stronger the weighting. This dispenses with a separate treatment of non-monotonic, ambiguous characteristics. The ambiguities in the characteristics are automatically eliminated.
In order to carry out the method, use is made of an arrangement which comprises sensors which determine the pressure difference between suction side and pressure side of the pump. Furthermore, use is preferably made here of a machine for determining the effective power and actuation frequency of the motor of the pump. Preferably, this is a frequency converter which supplies these data during operation.
The arrangement comprises at least one unit which captures these measurement data. This is an electronic evaluation unit. The unit comprises a data memory, in which delivery head-delivery flow relationships and power-delivery flow relationships of the pump are stored. The unit has appropriate signal inputs.
Preferably, the probability density function for the delivery head or for the power is calculated by way of functions which have a pronounced maximum. By way of example, use can be made of a triangle function. Here, a normal distribution density function, referred to as a Gaussian function below, was found to be particularly advantageous as a probability density function for the delivery head and for the power.
According to the invention, the probability density function for the delivery head is applied to the delivery head-delivery flow relationship: each delivery flow value is assigned the probability density of the associated delivery head by means of the H(Q) characteristic. A first probability density function for the delivery flow emerges from subsequent normalization, carried out in such a way that the integral over the probability density function is 1.
In a manner analogous to the preceding step, the probability density function for the power is applied to a power-delivery flow relationship in a further step: each discrete delivery flow value is assigned the probability density of the associated power by way of the P(Q) characteristic. A second probability density function for the delivery flow emerges by the subsequent normalization, which is carried out in such a way that the integral over the probability densities is 1.
In a particularly expedient variant of the method, the combined probability density function of the delivery flow is ascertained by multiplying the first probability density function by the second probability density function of the delivery flow and by a subsequent normalization. In a particularly expedient variant of the method, the delivery flow is ascertained as expected value of this probability density function. Alternatively, the sought-after delivery flow may also be determined as the delivery flow associated with the maximum value of this function.
Errors as a consequence of measurement uncertainties are minimized by the multiplicative link of the two probability density functions for the delivery flow.
In one variant of the invention, the power and the rotational speed are ascertained from the motor actuation frequency and the effective power by an algorithm.
In one variant of the invention, the H(Q) characteristics and/or P(Q) characteristics are interpolated and/or extrapolated. To this end, a certain number of nodes are predetermined. By way of example, a linear interpolation may be carried out between the nodes. In order to keep the error as low as possible, a number of nodes which is as large as possible is used.
Alternatively, the characteristics may also be stored as a function, for example in the form of a polynomial.
According to one configuration of the invention, the power-delivery flow relationship and an ascertained value of the power of the known delivery flow are brought into correspondence by an offset correction.
It was found that particularly accurate results for the delivery flow are ascertained in the method according to the invention if the P(Q) characteristic experiences a rotational speed-dependent offset correction. To this end, the power determined for a specific delivery flow Q, preferably Q=0, is compared to the value of the P(Q) characteristic. The deviation is then adapted in the style of a single-point calibration.
Instead of the described conversion of the delivery head and shaft power to the rated rotational speed, there may also be a conversion of the delivery head and the shaft power to a different specific rotational speed. Alternatively, instead of the conversion of the delivery head and the shaft power to a predetermined rotational speed, there may be a conversion of the characteristics, i.e. of the delivery flow-delivery head relationship of the pump, of the power-delivery flow relationship of the pump and the probability density functions for the delivery head and the shaft power, to the current rotational speed of the pump in accordance with the known affinity laws.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of one or more preferred embodiments when considered in conjunction with the accompanying drawings.